The “Cell Assembly Theory”, introduced in 1949 by Donald Hebb in his milestone The Organization of Behaviour [1]}, looks at learning processes as collective features of neurons and can be effectively summarized by the famous prescription “neurons that fire together wire together”. Since then, Hebb's learning has become a prolific cornucopia for modeling neural networks [2]}, [3]}. In particular, the Hopfield model [4]}, where the Hebbian scheme is implemented mathematically, constitutes a paradigmatic model which has been attracting much attention since the mid-eighties, following the seminal investigation by Amit, Gutfreund and Sompolinsky [4]} based on statistical-mechanics tools. Indeed, after the breakthroughs by Parisi [6]} and coworkers [7]}, [8]} at the turn of the seventies in the eighties, statistical mechanics of disordered systems was established as the theoretical reference where spontaneous information processing capabilities of Hebbian-like neural networks can be fruitful inspected.
Along this way important achievements have been collected (see e.g.  [9]}, [2]}), and nowadays Hebb's rule is usually the starting point when getting acquainted with (bio-inspired) neural networks and related modelling. However, Hebb's rule did not appear out of the blue, rather it was an enlightened synthesis of decades of meticulous inspections in neurophysiology and psychology, whose origins have to be traced back to the
systematic studies of Ivan Pavlov on Classical ConditioningIt is worth noting that, roughly in the same years, also Thorndike [11]} and Twitmyer [12]} understood the core idea behind Classical Conditioning but they drew minor attention from the scientific community at that time., which greatly inspired Donald HebbIt is reported that Boris Babkin, a student of Pavlov's, spurred Donald Hebb to deepen Classical Conditioning..
Despite this closeness, the two theories – Hebb's learning based on neuron-activity correlation and Pavlov's learning based on conditioning by stimuli – had quite distant fates, at least in the context of theoretical modelling, the former being by far much more represented in the mathematical and physical literature (as for the latter, one should still recall significant contributions by Estes [13]}, Hull and Spence [14]}, and modern extensions by Rescorla-Wagner [15]} and Mackintosh [16]}). Hereafter we aim to provide a mathematical description of Classical Conditioning, whence one could appreciate how Pavlov implies Hebb: this bridge is the main focus of the present workInspiring ideas about this connection between Pavlov and Hebb from a modeling perspective are due to Francesco Guerra, see [17]}, [18]}..
